The two ways to look at sound

This is the most important chapter in the book. Once it clicks, almost every tool in every audio program will suddenly make sense.

The problem with the waveform

The waveform — that wiggly line of heights — tells you when things are loud, but not what they are. A hiss, a hum, a voice and a cymbal are all stirred into the same line. Trying to remove the hiss by editing the waveform is like trying to remove the salt from a soup with a fork.

What you really want is to separate the sound by pitch: put all the low rumble in one pile, the mid-range voice in another, the high hiss in a third. Then you could lower the hiss pile without touching the voice pile. That second view exists, and it’s called the frequency view, or the spectrum.

Splitting sound into pure tones

Here’s the deep idea, discovered by a mathematician named Fourier two centuries ago: any sound, however complicated, can be rebuilt by adding together a bunch of simple, pure tones — like the steady note of a tuning fork — each at its own pitch and its own loudness.

So a voice isn’t one thing; it’s a recipe: “a little bit of this low tone, a lot of this mid tone, a touch of that high tone…” Hiss is its own recipe: “a tiny, even sprinkle of every high tone at once.” A 60-cycle hum is the simplest recipe of all: “one specific low tone, and nothing else.”

The machine that takes a chunk of sound and reads off its recipe — how much of each pitch is present — is the Fourier transform, and the fast version every program uses is the FFT (Fast Fourier Transform). You will see “FFT” in the settings of every serious audio tool. Now you know what it means: split this sound into its ingredient pitches.

The spectrogram: the picture you’ll actually see

A single FFT reads the recipe of one short moment. But sounds change — a voice moves from word to word. So tools chop the audio into many short, overlapping slices (a few hundredths of a second each), take the FFT of every slice, and stack the results side by side. This sliding-window approach has a name — the Short-Time Fourier Transform, or STFT — and its picture is the spectrogram.

A spectrogram is a heat-map of sound: time runs left-to-right, pitch runs bottom (low) to top (high), and brightness shows how much of each pitch is present at each moment. On a spectrogram:

• A hum is a steady horizontal line low down — one pitch, always there.
• A voice is a shifting stack of bands in the middle that wobble as words change.
• Hiss is a faint, even haze across the entire top.
• A click is a thin vertical streak — a single instant where every pitch flares at once.

 pitch
  high ┤ ░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░   ← hiss: faint haze, everywhere, always
       │ ░░░░░░░░░░░ █ ░░░░░░░░░░░░░░░░░░░
   mid ┤ ▓▓▓▓   ▓▓▓  █  ▓▓▓▓▓   ▓▓▓▓▓▓      ← voice: bright bands that move
       │  ▓▓▓  ▓▓▓▓  █   ▓▓▓    ▓▓▓          with the words
   low ┤ ━━━━━━━━━━━━█━━━━━━━━━━━━━━━━━━━   ← hum: one steady line, low down
       └──────────────────────────────►  time
                     ↑ click: a vertical streak (one instant, all pitches)

Suddenly the soup is unstirred. The hiss, the hum, the voice and the click are in visibly different places. That is why nearly every restoration tool works in the frequency view: in the spectrogram, the problem and the wanted sound usually sit in different spots, so you can lower one without harming the other.

The loop almost everything uses

Most of cathar’s “reduce” tools, and the equivalent tools in every professional program, run the same three-step loop, over and over, on each short slice:

1. Analyse — FFT the slice into its recipe of pitches.
2. Modify — turn down (or rebuild) the parts you don’t want.
3. Resynthesise — add the pitches back together into a cleaned slice, and glue the slices back into a waveform (a careful blend called overlap-add).

flowchart LR
    A["one short slice<br/>of the waveform"] --> B["FFT<br/><i>analyse</i><br/>split into pitches"]
    B --> C["<b>modify</b><br/>turn down / rebuild<br/>the unwanted pitches"]
    C --> D["inverse FFT<br/><i>resynthesise</i><br/>add pitches back"]
    D --> E["overlap-add<br/>→ cleaned waveform"]

Cathar uses a 2,048-sample slice with a 75% overlap between neighbours and a gentle taper (a Hann window) so the joins are seamless. Those exact numbers don’t matter to you; the shape of the idea does. Analyse → modify → resynthesise. Hold onto it. Every “de-noise / de-hum / de-reverb / de-ess” tool in this book is a different idea for that middle modify step. The rest is plumbing.

How the big tools do it

Every audio program you’ve heard of lives in this same two-view world. The spectrogram in iZotope RX — the industry-standard restoration suite — is the centrepiece of its interface; you literally paint on it to fix problems. Adobe Audition has a “Spectral Frequency Display” that’s the same idea. Free Audacity shows a spectrogram view too. They all rely on the FFT/STFT loop above. The differences between cheap and expensive tools are almost never about this foundation — they’re about how cleverly the modify step decides what’s noise and what’s signal, which is exactly what the next chapters are about.